27.1  a) 3*4*sin(pi/3)
      b) 5*7*sin(arccos(-21/(5*7)))
      c) 3*6*sin(pi)
      d) a*b*sin(k*pi)

27.2  Cross[(2,-3,1),(5,1,-2)], Cross[(0,0,0),(2,-3,1)], Cross[3(2,-3,1)-2(5,1,-2),(2,-3,1)+5(5,1,-2)]

27.4  b) 1/2*sqrt(Cross[(1,-3,2),(-3,-1,-4)].Cross[(1,-3,2),(-3,-1,-4)])
      c) 1/2*sqrt(Cross[{2,2,0},{1,1,0}].Cross[{2,2,0},{1,1,0}])
      d) 1/2*sqrt(Cross[{3,-3,0},{-2,-1,0}].Cross[{3,-3,0},{-2,-1,0}])

27.5  1/2*(8*(6*6*sqrt(2)/2))

27.6  sqrt(1^2+2^2) = sqrt(2^2+1^2)
      1*2+2*(-1)
	  1/sqrt(5)*Cross[{1,2,0},{2,-1,0}]

27.7  -Cross[(2,3,-1),(1,-1,3)]
      sqrt(Cross[(2,3,-1),(1,-1,3)].Cross[(2,3,-1),(1,-1,3)])

27.8  Cross[(11,10,2),(4,0,3)]/sqrt(Cross[(11,10,2),(4,0,3)].Cross[(11,10,2),(4,0,3)])

27.10 a) Det[{-3,4,-7},{1,2,5},{1,-4,5}]
      b) 4*3*sin(5*pi/6)*5*cos(pi)
      c) -2*4*sin(pi/2)/3*3^2

27.11 |Det[{3,6,3},{1,3,-2},{2,2,2}]|/6
      9/(1/2*sqrt(Cross[(3,6,3),(1,3,-2)].Cross[(3,6,3),(1,3,-2)]))

27.12 solve 1/6*|Det[{1,-1,2},{0,-2,4},{-2,x-1,1}]| = 5

27.13 Det[{-1,-1,6},{-2,0,2},{1,-1,4}]